The entrance region constitutes a considerable fraction of the channel length in miniaturized devices. Laminar slip flow in microchannel plate fin heat sinks under hydrodynamically developing conditions is investigated semi-analytically and numerically in this paper. The semi-analytical model for the pressure drop of microchannel plate fin heat sinks is obtained by solving the momentum equation with the first-order velocity slip boundary conditions at the channel walls. The simple pressure drop model utilizes fundamental solutions from fluid dynamics to predict its constitutive components. The accuracy of the model is examined using computational fluid dynamics (CFD) simulations and the experimental and numerical data available in the literature. The model can be applied to either apparent liquid slip over hydrophobic and superhydrophobic surfaces or gas slip flow in microchannel heat sinks. The developed model has an accuracy of 92 percent for slip flow in microchannel plate fin heat sinks. The developed model may be used to predict the pressure drop of slip flow in microchannel plate fin heat sinks for minimizing the effort and expense of experiments, especially in the design and optimization of microchannel plate fin heat sinks. Fluid flow in microchannels has emerged as an important research area. This has been motivated by their various applications such as medical and biomedical use, computer chips, and chemical separations. The high level of heat dissipation requires a dramatic reduction in the channel dimensions. The high flux heat dissipation from high-speed microprocessors provided the impetus for studies on heat transfer in microchannels . It is wMicrochannels are the fundamental part of microfluidic systems. In addition to connecting different devices, microchannels are also utilized as biochemical reaction chambers, in physical particle separation, in inkjet print heads, in infrared detectors, in diode lasers, in miniature gas chromatographs, in aerospace technology, or as heat exchangers for cooling computer chips. Understanding the flow characteristics of microchannel flows is very important in determining the pressure drop, heat transfer, and transport properties of the flow for minimizing the effort and expense of experiments, especially in the design and optimization of microchannel plate fin heat sinks. Microchannel heat sinks have received considerable attention owing to their high surface-area-to-volume ratio, large convective heat transfer coefficient, and small mass and volume. For the effective design and optimization of microchannel heat sinks, it is significant to understand the fundamental characteristics of fluid flow and heat transfer in microchannels.The purpose of this paper is to study the pressure drop characteristics of fluid flow through microchannel plate fin heat sinks. The developing slip flow friction factor Reynolds number parameter is determined for the laminar regime. Following this, there we analyze the pressure drop through microchannel plate fin heat sinks.In this study, the developing laminar flow is analyzed through plate fin heat sinks with velocity slip boundary conditions, and semi-analytical closed-form solutions are obtained for the friction factor and Reynolds number product and pressure drop in terms of the channel aspect ratio, channel length, hydraulic diameter, Reynolds number, and modified Knudsen number. The primary goal of the present paper is to provide a general simple pressure drop model of fluid flow through microchannel plate fin heat sinks.Kn) relates the molecular mean free path of gas to a characteristic dimension of the duct. The Knudsen number is very small for continuum flows. However, for microscale gas flows, the gas mean free path becomes comparable to the characteristic dimension of the duct. Rarefaction effects must be considered in gases in which the molecular mean free path is comparable to the channel’s characteristic dimension. The continuum assumption is no longer valid, and the gas exhibits non-continuum effects such as velocity slip and temperature jump at the channel walls. Traditional examples of non-continuum gas flows in channels include low-density applications such as high-altitude aircraft or vacuum technology. The recent development of microscale fluid systems has motivated great interest in this field of study. Microfluidic systems should take into account slip effects. There is strong evidence to support the use of Navier–Stokes and energy equations to model the slip flow problem, while the boundary conditions are modified by including velocity slip and temperature jump at the channel walls. The slip length can be interpreted as the distance from the wall that the slip velocity profile extends to if extrapolated away from the boundary. In gas flows, the slip length is related to the Knudsen number, while in liquid flows, the slip length depends on the surface microstructure [The Knudsen number  and mean velocity The geometry of a microchannel heat sink is shown in Po is interpreted as the fully developed dimensionless average wall shear. The fully developed mean wall shear stress may also be related to the pressure gradient by means of the force balance The above grouping ξ is the non-dimensional channel length. This analysis demonstrates that inertial forces are quite important for short ducts where ξ << 1. The fluid flow behavior in the developing region differs from that in the fully developed region. The parameter We examine the momentum equation and consider the various force balances using the method of scale analysis. Comparing the force scale between friction and inertial forces, we obtain the following relation: fapp, must be utilized to calculate the factual pressure drop. The apparent flow friction factor is used in this paper since it incorporates the pressure drops caused both by the wall shear stress due to the significant velocity gradient normal to the wall and by the momentum flux variation due to the change of velocity field from a uniform profile at the inlet to a specific profile downstream in the channel. Researchers have generally assumed microchannel heat sink flows to be fully developed, ignoring entrance effects; therefore, care should be exercised as most of the statements, formulas, and charts are valid only for long ducts. The long duct criterion will be discussed later in this paper.In many practical applications, the length of the channel in the developing region therefore forms a major portion of the flow length through a microchannel. To account for the developing region, the pressure drop equations are presented in terms of an apparent friction factor. The apparent friction factor accounts for the actual pressure drop due to friction and the developing region effects. It represents an actual value of the friction factor over the flow length between the inlet and the location under consideration. Therefore, the apparent friction factor, cK and eK represent the contraction and expansion loss coefficients due to area changes. The friction factor used in Equation (3) is the apparent friction factor and accounts for the developing region. Fluid flow modelling in a plate fin heat sink is essentially a simultaneously developing hydraulic and thermal boundary layer problem in rectangular ducts. The flow may become fully developed if the heat sink channel is sufficiently long in the flow direction or with relatively small fin spacing; however, this is very unlikely for microchannel heat sinks for electronic cooling applications. The hydrodynamically developing flow can become quite important in microchannels. Due to the often-short lengths, the developing flow could dominate the entire flow length of the microchannel. When considering the developing flows, the pressure drop is now related to an apparent friction factor. The apparent friction factor, fapp, for a rectangular channel may be computed using a form of the model developed by Duan and Muzychka [G(ξ) representing additional pressure drop which exceeds the fully developed pressure drop. Thus, the difference between the apparent friction factor and Reynolds number product over a length and the fully developed friction factor and Reynolds number product is expressed in terms of an incremental pressure defect G(ξ):Generally, there are three main components that contribute to the overall pressure drop. The inlet and exit losses need to be quantified for the microchannel. The hydrodynamic frictional pressure loss needs to be carefully evaluated. Summing all of the frictional and inlet and exit dynamic losses, the total pressure drop model function is given in terms of Bernoulli’s equation,Muzychka  for deveMuzychka  demonstrThe commonly used customary incremental pressure drop number  is given byξ >> 1, the fully developed flow momentum equation in Cartesian coordinates reduces to the formThe Navier–Stokes equations are assumed to be valid in their traditional form, and wall slip is merely modeled through a modification of the boundary condition. Rectangular geometries are of particular interest in microfluidics applications. We may now examine the solution for rectangular ducts for slip flow. A schematic diagram of the rectangular cross section is showed in λ generally denotes the slip length for either gases or liquids, which is defined based on the physics of the fluid flow. The slip length can be used to characterize the type of flow in channels: if λ = 0, the flow is no-slip flow; if λ = λ represent partial slip flow. For gas slip flow, Maxwell’s first order correction givespλ is the molecular mean free path. The constant σ denotes the tangential momentum accommodation coefficient. Equations (11) and (12) are mathematically equivalent to the first-order correction commonly employed in the analysis of rarefied gas flow in the slip flow regime. It is convenient to define a modified Knudsen number as Kn* = Kn(2 − σ)/σ. A nondimensional number similar to the modified Knudsen number (Kn*) can be defined for liquid slip flow, i.e., the ratio of slip length to a characteristic dimension of the flow field, and the presently developed model can then be utilized for liquid flows over superhydrophobic surfaces to predict pressure drop. To look at it from a slightly more general mathematical point of view, when the no-slip condition on the solid surfaces is partially relaxed, the molecular mean free path and the term involving the accommodation coefficient  are a set of eigenfunctions. This solution satisfies the boundary condition, Equation (9). Furthermore, substituting the velocity solution into the boundary condition, Equation (7), we obtainFollowing Ebert and Sparrow , using tThe characteristic length scale in the present analysis is defined as the hydraulic diameter.Thus,nδ can be obtained from Equation (16). Finally, the velocity distribution is obtained as follows:The eigenvalues The mean velocity is found by integration of Equation (17) across the section of the duct.We can obtain the friction factor and Reynolds number product from the above equations in terms of the aspect ratio and the slip coefficient.ε→0:The limit of Equation (19) corresponds to a parallel-plate channel for *Kn→0. The relationship between the flow friction coefficient, f, and Reynolds number, Re, for a fully developed laminar flow regime in a rectangular channel is only a function of the aspect ratio and may be calculated as follows:It can also be demonstrated that Equation (19) reduces to its no-slip flow limits as ε = 1, which gives an fRe value 0.7 percent below the exact value. When greater accuracy is desired, two terms are absolutely enough due to very rapid convergence, and the largest error is less than 0.05%. Considering only the two terms of the exact series, Equation (21) givesExamination of the single-term solution reveals that the single-term approximation is accurate enough for engineering applications. The largest difference occurs when This equation is founded on theory and is more accurate compared to those obtained by curve fitting .α depends on the duct geometry.The slip flow friction factor results can be presented conveniently in terms of the normalized Poiseuille number. The Poiseuille number reduction depends on the geometry of the cross section. It is convenient that the Poiseuille number results are expressible to good accuracy by the relationα are derived from a least-square fit of the Poiseuille number results. The constants α are a weak function of the aspect ratio, and the data points are fitted to a simple correlation [For rectangular ducts, the constants relation :(24)α=11Then, Equation (19) can be simplified to facilitate practical application as follows:*Kn but independent of the cross-sectional geometry [ξ ≤ 0.001), fappRe is nearly equivalent and independent of duct shape. The boundary layer behavior in the tube entry is substantially identical to that on a flat plate. At the entrance of the duct, the velocity boundary layer starts developing at each wall under the imposed flow acceleration. As long as the thickness of the boundary layer is small compared to the duct dimensions, the boundary layers from different walls do not affect each other appreciably. This explains why very near the inlet of ducts, fappRe is nearly equivalent and independent of duct shape. As the boundary layer develops further downstream (ξ > 0.001), the effects of geometry become gradually more pronounced. The incremental pressure defect G(ξ) for a rectangular channel may be computed using a form of the model developed by Duan and Muzychka [It is found that the entrance friction factor and Reynolds number product is of finite value and dependent on geometry . Duan angeometry  also demMuzychka  for deveν. While typical microflows are characterized by Re < 100, in a few microfluidic applications such as micro heat exchangers and micromixers, the Reynolds number can reach the order of a few hundreds. It is emphasized that several eigenvalues are sufficiently accurate for all values of ξ of engineering interest. The negative exponentials cause rapid convergence, especially if ξ is not too small. As an illustration, for a practical engineering application limit of ξ ≥ 0.01, only two terms in the summation are really required. It can be demonstrated [ξ→0 asymptote ξ→Equation (26) is nearly independent of the duct shape and may be used to calculate the friction factor and Reynolds number product for the short asymptote of rectangular ducts for slip flow. We will take advantage of the asymptotic limit for developing an approximate model for predicting pressure drop for plate fin heat sinks. The eigenvalue equation :(27)αiJ0nstrated  that theφ = 2b/(2b + t). The graphs of experimental data for laminar flow in Reference [For the inlet and exit pressure losses for a heat sink, Kays and London  provide eference  have beefappRe in slip flow for various aspect ratios of the rectangular cross section. From an inspection of the graphs, it is seen that fappRe monotonically decreases in the entrance region, and fappRe decreases as the modified Knudsen number increases for the same aspect ratio. The effect of increasing Kn* is to decrease the apparent friction and pressure drop over the channel length very significantly. In addition, the fappRe values decrease with increasing ε for the same Kn*. Moreover, it is obvious that the pressure gradient for a slip flow is less than that for the corresponding no-slip flow. This effect of the developing region is significant for microchannel plate fin heat sinks.The developing apparent friction factor and Reynolds number parameter as a function of aspect ratio and modified Knudsen number is illustrated clearly in some graphs. ξ is the proper parameter. ξ. The effects of the aspect ratios on the pressure drop in the slip flow region are investigated in The values in the entrance region are larger than those in the fully developed region, which demonstrates the critical importance of the entrance region in determining the pressure drop characteristics in microchannel heat sinks. To take into account the entrance effects on the overall pressure drop in the microchannel region, clearly, the dimensionless developing length Numerical simulations were conducted using the commercial solver ANSYS Fluent 14.0  with user-defined functions. A structured mesh composed of rectilinear elements was constructed in a preprocessor to define the flow domains. The governing equations were solved with a commercial implementation of the finite volume method using a pressure-based solver and the SIMPLE algorithm. The slip boundary condition was implemented as a user-defined function in FLUENT. The solution algorithms were considered converged when the convergence criterion was satisfied. Local mesh refinement was performed using FLUENT’s grid adaption utility at the flow inlet.fappRe does not depend on the dimensionless hydrodynamic length when the dimensionless hydrodynamic length is approximately unity, which should be the long duct criterion. In the range of ξ < 0.06, the fappRe decreases rapidly with increasing ξ due to the finite thickness of the boundary layer at the microchannel entrance region. With an increase of ξ, the fappRe has a comparatively gently downward tendency.Shah and London  presentefappRe with the non-dimensional flow distance and the comparison between the proposed model Equation (28) and slip flow numerical results when the aspect ratio ε = 1. It is found that the model predictions agree with our numerical results. The maximum deviation between the numerical results and the proposed model is less than 2.6%. It is clear that Equation (28) characterizes the pressure drop in microchannel plate fin heat sinks. The maximum deviation of exact values is less than 8 percent. The pressure drop may be predicted from Equation (28), unless greater accuracy is desired. The developed pressure drop model may be suitable for the parametric design of and optimization studies on microchannel plate fin heat sinks.The fluid flow behavior in the developing region differs from that in the fully developed region. The parameter ξ values, with low-aspect-ratio ducts reaching it a little earlier. The fully developed flow is attained when ξ is approximately 1 for rectangular ducts, as seen from these figures. The dimensionless developing length ξ is the proper parameter to take into account the entrance effects on the overall friction factor and pressure drop. The friction factor is higher in the developing flow region. Finally, beyond the entry region, the conventional theory for fully developed flow applies. Generally, the entrance region effects are less than 2% for the friction factor and Reynolds number product and can be neglected when It can be seen that fully developed flow is attained at different This paper investigated pressure drop in the fluid flow in microchannel plate fin heat sinks. The paper deals with issues of hydrodynamic flow development in microchannel plate fin heat sinks. A model was proposed for predicting the pressure drop in microchannel plate fin heat sinks for developing slip flow and continuum flow. The accuracy of the developed model was found to be within 5 percent for practical configurations. Errors of this magnitude are acceptable for most engineering purposes. The model can be considered adequate and sufficiently reliable to analyze the pressure drop in microchannel plate fin heat sinks. As for slip flow, no solutions or tabulated data exist for microchannel plate fin heat sinks, so this developed model may be used to predict pressure drop in slip flow in microchannel plate fin heat sinks. The developed model is simple and founded on theory, and it may be used by the research community for the practical engineering design and optimization of microchannel plate fin heat sinks.The goal of this investigation was to predict the pressure drop of the flow in microchannel plate fin heat sinks. The fully developed flow or long duct criterion for pressure drop is given. It is clearly shown that the entrance effects could be the source of the often-conflicting results previously reported in the literature.


Re < 1000), channel aspect ratio (0 < ε < 1), and Knudsen number (0.001 < Kn < 0.1) on the dimensionless hydrodynamic entrance length, and the apparent friction factor, and Reynolds number product, are examined in detail. The numerical solution of LBM can recover excellent agreement with the available data in the literature, which proves its accuracy in capturing fundamental fluid characteristics in the slip-flow regime.Developing a three-dimensional laminar flow in the entrance region of rectangular microchannels has been investigated in this paper. When the hydrodynamic development length is the same magnitude as the microchannel length, entrance effects have to be taken into account, especially in relatively short ducts. Simultaneously, there are a variety of non-continuum or rarefaction effects, such as velocity slip and temperature jump. The available data in the literature appearing on this issue is quite limited, the available study is the semi-theoretical approximate model to predict pressure drop of developing slip flow in rectangular microchannels with different aspect ratios. In this paper, we apply the lattice Boltzmann equation method (LBE) to investigate the developing slip flow through a rectangular microchannel. The effects of the Reynolds number (1 <  In recent years, rapid development in manufacturing technologies, together with a motivation toward MEMS ,2,3,4, h> 10). Here we pay special attention on the slip flow, where the rarefaction effect may be significant, and the conventional Navier–Stokes simulation can be used with appropriate s velocity slip boundary conditions. This regime has attracted extensive attention from the engineering research community because of its significance associated with many of the practical microfluidic devices. It has been the subject of many studies employing continuum modeling to examine the slip-flow convection at the microscale [Rarefaction effects, usually characterized by the Knudsen number, which is defined as the ratio of the molecular mean free path of gas to a characteristic dimension of flow domain. According to the value of croscale ,6,7,8 ovLiquid slip is very important in microfluidic devices with a superhydrophobic surface because it reduces the required pressure in pressure-driven flows. Due to the lack of molecular based theory of liquids, a nondimensional number  has attracted a variety of researchers to apply it to simulate microchannel flows ,24,25,26Chen and Doolen  first apDorari et al.  investigSucci  proposedr = 0.59, in the specular bounce-back scheme. They exhibited a mathematical formulation of kinetic boundary conditions for LBE schemes, in terms of reflection, slip, and accommodation coefficients.Sbragaglia and Succi  simulateKn-τ relation that differs from that of Lim et al. [With an equilibrium wall boundary condition, Lee and Lin  employedm et al.  by a facm et al. .Jeong et al.  applied Tang et al.  later siAs shown by Guo and Zheng , VerhaegMontessori et al. ,39,40,41articles ,43 have Owing to its kinetic characteristics and distinctive advantages over conventional numerical methods, the LBM has been a new potential tool and attained great success in studying microflows. To the authors’ best knowledge, there are no systematical investigations reported in using LBM to study the developing laminar flow for rectangular microchannels in the slip regime, especially focusing on the aspect ratios and hydrodynamic development length of rectangular microchannels.In the open literature, the only fluid flow data available for the laminar entrance region of rectangular microchannels may be the model proposed by Duan and Muzychka ,45, whicThe aim of this paper is to analyze hydrodynamic characteristics of the entrance region for laminar flow in three-dimensional rectangular ducts with aspect ratios from 0.1 to 1. By means of LBE method, we concentrate on the effects of rarefaction on the hydrodynamically-developing flow and pressure drop in the entrance region for rectangular ducts. In the present investigation, the role of the Reynolds number, aspect ratios and Knudsen number on the hydrodynamic development length of rectangular microchannels is also examined and investigated.It is assumed that this internal flow is three-dimensional, incompressible, laminar, isothermal, and steady in the entrance region of rectangular microchannels. There exists a velocity slip on the wall. Assuming the working fluid is a Newtonian fluid, according to the proposed hypotheses, the continuity equation and momentum equation in its most common general form are:λ is the molecular mean free path, n.The velocity distribution must be satisfactory for the slip boundary condition at the walls. According to gas kinetic theory, the gas velocity at the wall is different from the wall velocity, which is expressed in terms of the local velocity gradient at the wall. The first-order Maxwell boundary condition for the velocity at the wall is:Since the pressure gradients found in microchannels are quite high, the flow lengths are generally kept low. To account for the developing region, the pressure drop equations are presented in terms of an apparent friction factor For the slip flow entrance region problem, the available data are given by the approximately analytical solutions presented by Duan and Muzychka , where tHere, For the semi-theoretical analytical model, we can use Equation (10) to investigate the apparent friction factor and Reynolds number product for developing slip flow in rectangular ducts. With arbitrary aspect ratios and axial distances, it is of great convenience to calculate the apparent friction factor and Reynolds number product To demonstrate the utility of LBE method for simulating the three-dimensional flow in a rectangular channel, we consider the isothermal D3Q15 BGK-LBE  model  to derivFor the square lattice LBGK model D3Q15, the basic discrete-velocity Boltzmann kinetic equation is:Here i = 0), i = 1, 2, 3, 4, 5, 6), i = 7, 8, 9, 10, 11, 12, 13, 14), The equilibrium distribution By undertaking a multiscale technique, we can recover the macroscopic equations of the model. As a result, it is considered as a numerical solver of the Navier–Stokes equation.They are given by the continuity equation and the momentum equation:In the LBM simulation, we must give appropriately the relationship between the relaxation time erically .The mean free-path Therefore, with Equation (21) we have:τ and the kinematic viscosity of the fluid satisfy the relation In the LBGK model, As usual, the LBE method consists of two steps, collisions and streaming. After one time step The collision step without forcing function is:For a certain site, there are other particles coming from different directions, collision occurs among them at this site, and the original particle numbers moving in each direction will be changed. In a LBM simulation, such streaming and collision processes are repeated again and again until satisfied results are achieved.Correct boundary conditions are crucially important for the accuracy and stability of the LBM. In this work, assuming a uniform velocity at the inlet of the microchannel, and the pressure is known and equal to 1 atm at the outlet boundary. Two types of boundary conditions must be dealt with: (a) the slip boundary conditions at the walls, (b) velocity boundary conditions at the inlet and pressure boundary conditions at the outlet. In the LBE techniques this flow can be simulated with the bounce-back of the non-equilibrium approach originally proposed by Zou and He  at the iNon-equilibrium extrapolation scheme proposed by Guo et al.  is used When the flow encounters the slip-flow regime, the velocity slip occurs. The velocity slip near the wall plays an important role, which makes the implementation of boundary condition critical for the microflow simulation. For the wall boundaries, we apply the combined bounce-back and specular-reflection (CBBSR) boundary condition. The slip boundary conditions are given in the following form:ondition ,49,50,51o et al. ,49 pointc et al.  pointed x with the microchannel width on the z-axis, and with the theoretical maximum centerline fully-developed axial velocity on the x-axis The development of the three dimensional, laminar velocity profiles in the entrance region of a rectangular duct are investigated, the velocity profiles for aspect ratio As demonstrated in the analytical section, the pressure-drop results are presented conveniently in terms of the grouping apparent friction factor and Reynolds number product In this part, we use the calculated results from Equation (10) in Duan and Muzychka  as the rx+ values, with the low aspect ratio ducts reaching it earlier. As described earlier, initially, the change in Knudsen number (due to the density variation) plays a vital role in determining the friction coefficient behavior. In addition, compared with the traditional numerical methods for microflow simulation, such as the finite volume method, the computation effort of the lattice Boltzmann method may increase. An excellent agreement between the numerical and analytical results in the range 0.001 < Due to the relatively short lengths employed in microchannels, the influence of the entrance region cannot be neglected. The entrance region effects become more pronounced at smaller Knudsen numbers in part explaining the trend of decreasing Slip flow in the entrance region of rectangular microchannels was investigated numerically by Renksizbulut et al.  and Niaztal data  is from U is a function of the independent variables U can be estimated by Equation (32):To account for this discrepancy, a careful analysis of the experimental uncertainty in this study is critical to the interpretation of experimental data and exploration of deviation from the LBE method. An uncertainty analysis is performed on relevant parameters using the root sum square method described by Moffat . AssuminUncertainty analysis provides a reasonable method to evaluate the significance of the scatter on experiments. This is a powerful tool in locating the source of trouble in an experiment.For incompressible flow through horizontal pipes or channels of constant cross-sectional area, the friction factor and Reynolds number product can be expressed as follows:Equation (34) offered for the discrepancy of the fully developed laminar flow’s predictions and that obtained for an incompressible developing flow with the entrance section effects. The final expression for uncertainty in estimating LK(x+) represents the losses due to the hydrodynamic developing region. The product of the measured friction factor and Reynolds number can then be compared to the theoretical value for laminar flows. For flows in ducts of various cross-sections, a relationship of the form According to Equation (35), the experimental uncertainties in It can be seen that the most dominant terms in the The flow-developing region is very important, particularly in microchannels, when dealing with fluid flow within micro-channels, as these ducts are usually very short. In most applications, the short length of the channels is not enabling the flow to reach the fully developed regime. Thus, the length of the hydrodynamic developing region Several hydrodynamic entrance length studies have been explored both experimentally and numerically. Regarding numerical studies for rectangular ducts and parallel plate channels, results found by groups, such as Han , FlemingFor low Reynolds numbers one can consider entrance length correlations given by Atkinson et al. , Chen 5, Durst eChen  proposedRe < 100:Durst et al.  employedRe, which considered the effects of slip flow:Duan and Muzychka  applied Re is high, an approximately linear curve is depicted. However, at very low Re, Re.These correlations were established in common through a combination of the creeping flow and boundary-layer type solutions. Looking at these above correlations, when Re < 1000; however, a limited range of rectangular channel aspect ratios Re range of 0.5–200. Galvis et al. [Re < 200), hydraulic diameter  indicates that the entrance length has a rational relationship with the Reynolds number when the Reynolds number is small. The entrance length does not vanish as i et al. . It is fIn this paper, we have performed an investigation in slip flow through a rectangular microchannel using an improved incompressible LBGK D3Q15 model. The combined effects of aspect ratios and rarefaction on friction distribution characteristics have been investigated by employing the model. Our numerical results show that the entrance friction factor and Reynolds number product is of finite value and that the friction factor and Reynolds number product reduces with the decrease in Knudsen numbers and the increase in the channel aspect ratios. Various comparisons are presented among the available literature, including the numerical, experimental, and the semi-theoretical analytical data, which are in excellent agreements. Note that the solutions of the linearized Boltzmann equation are remarkably close to analytical results by solving the Navier–Stokes equation with slip boundary conditions in the slip regime. This means that the lattice Boltzmann method with a scheme of combining the bounce-back reflection with specular reflection applying to the boundary condition treatment can be capable of predicting the slip flow at the entrance region well.Re < 1000 under slip condition. The entrance length generally increases with the increase of In addition, numerical simulations have been used to study the developing flows in rectangular microchannels, focusing on the entrance length and its dependence on the Reynolds number and channel aspect ratio. Novelty correlation for the entrance length was proposed for rectangular channels with The results presented here are remarkable because they uncover the effects of rarefaction and aspect ratios on flow behavior at the entrance region in the slip regime which were not systematically reported earlier. These detailed results can also be used for benchmarking future microdevice designing. Furthermore, the present study serves as a baseline case for understanding transition flow in complex microchannels.


ABP). We have challenged its anti-inflammatory and immuno-modulatory properties in a robust rat model of acute uveitis induced by lipopolysaccharide (LPS). We show that dendrimer ABP at 2 µg/eye is as efficient as the “gold standard” dexamethasone at 20 µg/eye. We have demonstrated that the effect of dendrimer ABP is mediated at least through an increase of the production of the anti-inflammatory Interleukin(IL)-10 cytokine.Over the last decade, different types of dendrimers have shown anti-inflammatory properties in their own right. In particular, we have shown that poly(phosphorhydrazone) (PPH) dendrimers are able to foster an efficient anti-inflammatory response in human monocytes and can resolve the main physiopathological features of chronic arthritis in mice at 1 mg/kg. Here we afford new insights into the therapeutic potential of an azabisphosphonate-capped dendrimer (dendrimer  ABP  cells  [ABP, activates human monocytes in vitro [ABP has emerged as an anti-inflammatory “lead” dendrimer after the screening of the in vitro bio-activity of almost eighty dendrimers of different series [Poly(phosphorhydrazone) (PPH) dendrimers are synthesized according to a simple and efficient divergent strategy involving phosphorus-containing building blocks; and their surface functions can be easily modified to afford rationally-designed dendrimers . In thisABP , can act cancer) . We havein vitro  toward ain vitro ; and dent series ,7,8.per se [in vivo anti-inflammatory effects of dendrimer ABP in two mouse models of experimental arthritis: the IL1ra-/- and K/BxN models [ABP at 1 and 10 mg/kg weekly (for 12 weeks). Moreover, serum concentrations of pro-inflammatory cytokines and matrix metallo-proteases decreased significantly during treatment. We have also shown that per os administration of dendrimer ABP at 10 mg/kg/week for twelve weeks resolves experimental arthritis in this mouse model [ABP have also been demonstrated in the K/BxN serum transfer mouse model [ABP has become a serious drug candidate and is currently in pre-clinical development for the treatment of rheumatoid arthritis (RA) and potentially other inflammatory diseases [ABP in this highly competitive market, and to accelerate the bench to market process, it appeared appropriate to evaluate the activity of this compound in a relevant acute disease necessitating topical administration. In this regard, we have chosen the Endotoxin-Induced Uveitis (EIU) in the rat. This model is considered as a clinically relevant model for human anterior uveitis [ABP in the robust model of EIU in rats, in comparison with the “gold standard” dexamethasone.So far, only a few types of dendrimers have anti-inflammatory properties per se . In 2011N models . In IL1rekly for  weeks. Mdiseases ,14. In v uveitis ,16,17. I uveitis . The worABP for seven consecutive days following a single intra-vitreal injection in both eyes of rats. Three groups of three male Sprague-Dawley rats have been set up: the first group received the saline vehicle; the second and third groups received 20 µg (low-dose group) and 100 µg (high-dose group) of dendrimer ABP per eye, respectively.First, we have assessed the ocular tolerability of dendrimer During the study, no mortality and no effect on weight gain have been observed. Clinical observations revealed no detectable adverse effect on vision or eyesight in any of the treated animals. Gross clinical signs were limited to ocular observations of cloudiness in the vitreous of all animals of the high-dose group from day 1 to the end of the study, confirmed at necropsy. A slight cloudiness in the vitreous of one low-dose treated animal out of three was also noted from day 2 to the end of the study, but this cloudiness was not confirmed at necropsy two days later. Thus, cloudiness was found to be systematic and more important and persistent in the high-dose group than in the low-dose group.ABP-related.After dosing, McDonald-Shadduck scores elaborated from funduscopies and slit-lamp examinations (SLE) were consistently zero, with two exceptions when fluorescein staining of the cornea  was seen in one eye of an animal of the high-dose group at day 1 and in one eye of the low-dose group at day 6. The lack of any corneal findings during SLE examinations or histological studies suggests that the fluorescein staining did not indicate any underlying pathology but are likely spontaneous incidental background findings and not dendrimer Exhaustive histological studies were performed on eyeball tissue sections , and it ABP, while the 100 µg/eye dose was associated with inflammation in the vitreous. Having in hands these results, we have then decided to gain the “Proof of Concept” of the efficacy of dendrimer ABP in ophthalmology by the intra-vitreal route in a rat model of Endotoxin-Induced Uveitis (EIU). Increasing doses were chosen according to the tolerability study: 2, 10, 20 and 60 µg/eye, the latter being the only value over the NOAEL.Taking into account these data, we have considered the 20 µg/eye dose as a No Observed Adverse Effect Level (NOAEL) dose of dendrimer ABP in this model of acute inflammatory disease and challenged the “gold standard” dexamethasone. Six groups of six animals (n = 12 eyes) have been studied: vehicle only (group 1), dendrimer at 2 µg/eye (group 2), dendrimer at 10 µg/eye (group 3), dendrimer at 20 µg/eye (group 4), dendrimer at 60 µg/eye (group 5), dexamethasone at 20 µg/eye (group 6). Clinical scores of the six groups are presented in ABP-treated group has been excluded due to important hyphema, which could potentially modify clinical scoring, which led to work with n = 12 in all groups except in group 2 (n = 11).EIU is induced with injection of bacterial lipopolysaccharide (LPS) in the foot-pad of female albino Lewis rats and clinical scores are evaluated 24 h after induction. We have evaluated the effect of dendrimer ABP-treated eyes was statistically different from the mean score of vehicle group for the doses 2, 10 and 60 μg/eye with 33% (p < 0.01), 23% (p < 0.05) and 29% (p < 0.05) reduction, respectively. The mean clinical score of both eyes from dexamethasone-treated group was statistically reduced compared to the score from saline vehicle treated group with 49% (p < 0.001). Thus, these results show that a single intra-vitreal administration of dendrimer ABP at the time of LPS injection induces a significant reduction of ocular inflammation at the doses of 2, 10 and 60 µg/eye but does not exert any anti-inflammatory effect at the dose of 20 µg/eye, suggesting an inverse dose-response effect. It is important to note that the tolerability study revealed that administration of the molecule could induce sub-acute inflammation at the site of injection. Considering the small time scale of the assay (24 h), one can assume that the intrinsic anti-inflammatory properties of dendrimer ABP can be temporarily thwarted by the topical administration. Despite the fact that this effect could not be fully rationalized, this series of results show that in the most favorable case the effect of dendrimer ABP is not statistically different from the effect of the “gold standard” dexamethasone. In fact, the difference in the mean values of the two groups is not great enough to reject the possibility that the difference is due to random sampling variability (p = 0.1455).The mean clinical score evaluated 24 h after intra-vitreal saline vehicle administration was 3.83 ± 0.21. The mean clinical score of dendrimer ABP, we have assessed its effect at this dose by measuring local (in the aqueous humor and vitreous) and systemic (in the serum) concentrations of pro- and anti-inflammatory cytokines. Cytokine concentrations measured in aqueous humor and vitreous are presented in As the most important and significant effect is obtained with the dose of 2 µg/eye of dendrimer p < 0.05). On the contrary, TNF-α, IL-1β, IL-2 and IL-10 concentrations were not reduced in animals treated with 2 µg/eye of dendrimer ABP as compared to the one treated with saline vehicle alone.At 24 h post-induction and treatment, concentrations of pro-inflammatory/inflammatory cytokines TNF-α, IL-1β, IL-2 and anti-inflammatory cytokine IL-10 in ocular fluids were significantly reduced in the dexamethasone-treated group compared to the saline vehicle treated group (at least p < 0.001), due to the anti-inflammatory effect of the “gold standard” drug. In the dendrimer ABP-treated group, IL-6 and IL-17 concentrations tended to be reduced, although this reduction was not found significant. However, the statistical test indicates that the effect of dendrimer-ABP at 2 µg is not significantly different from that of dexamethasone (p > 0.05). Finally, it was found that the concentration of anti-inflammatory cytokine IL-4 and the concentration of pro-inflammatory cytokine IFN-γ in ocular fluids were not affected by dendrimer ABP or dexamethasone treatments at 24 h. In order to evaluate the influence of loco-regional applications on systemic inflammation marker response, we have then assessed the serum concentrations of IFNγ, TNFα, IL-2, IL-4 and IL-10  statements for the use of animals in ophthalmic and vision research ,21. OnlyABP per eye, respectively. On days 0 to 6, at approximately the same time on each day (±1 h), each animal was assessed by clinical observation and eye examinations. Ocular examinations included: funduscopy, slit-lamp examination (SLE) of the cornea using fluorescein dye enabling McDonald-Shadduck scoring. The McDonald-Shadduck Scoring System addresses: conjunctival parameters , aqueous flare  as presumptive evidence of breakdown of the blood-aqueous barrier; injection of secondary and tertiary vessels in the iris; cloudiness, relative area thereof, neo-vascularization and epithelial integrity (fluorescein labeling) of the cornea; integrity of the lens. On day 8, i.e., 2 days after the final ocular examination, all of the animals were sacrificed. Eyes were collected at necropsy, fixed in modified Davidson’s solution for 12 h, followed by 10% neutral buffered formalin and processed for histology. Hematoxylin-Eosin stained tissue sections were evaluated via light microscopy by a board-certified veterinary pathologist.The study consisted of three groups of three male Sprague-Dawley rats. On day 0, animals were weighed, anesthetized and administered by a single 5 µL intra-vitreal injection in both eyes. The first group received the saline vehicle (NaCl 0.9%), the second and third groups received 20 µg (low-dose group) and 100 µg (high-dose group) of dendrimer Salmonella typhimurium, Sigma-Aldrich, Saint-Quentin, France). Animals were treated immediately before EIU induction by a 5 µL intra-vitreal injection in both eyes of a saline solution (NaCl 0.9%) containing no active ingredient (group 1), or 2 µg of dendrimer ABP (group 2), or 10 µg of dendrimer ABP (group 3), or 20 µg of dendrimer ABP (group 4), or 60 µg of dendrimer ABP (group 5), or 20 µg of dexamethasone (group 6). Animals were examined by slit-lamp (SLE) at 24 h, i.e., the clinical peak of the disease in this model. The intensity of clinical ocular inflammation was scored on a scale from 0 to 5 for each eye. Grade 0 indicates no inflammation. Grade 1 indicates the presence of a minimal iris and conjunctival vasodilatation but without the observation of flare or cells in the anterior chamber (AC). Grade 2 indicates the presence of moderate iris and conjunctival vessel dilation but without evident flare or cells in the AC. Grade 3 indicates the presence of intense iris vessel dilation, flare and less than ten cells per slit-lamp field in the AC. Grade 4 indicates the presence of more severe clinical signs than Grade 3, with more than ten cells per slit-lamp field in the AC, with or without the formation of a hypopyon. Grade 5 indicates the presence of intense inflammatory reaction, fibrin formation in the AC and total seclusion of the pupil. Clinical evaluation was performed in a blinded manner. At the end of experiment, i.e., 24 h after LPS challenge, rats were anesthetized by intra-peritoneal injection of pentobarbital  then killed with a lethal dose of pentobarbital.Thirty-six female albino Lewis rats were randomly divided into six groups of six animals each. EIU was induced by a 100 µL footpad injection of sterile pyrogen-free saline solution containing 200 µg of LPS .ABP 2 µg and dexamethasone) were collected at the end of the experiment and stored at −80 °C. They were used for the simultaneous determination of five cytokine  levels with Cytometric Bead Array  on a FACS Calibur flow cytometer (BD Biosciences) according to the manufacturer’s instructions. The amounts of each of the cytokines were analyzed in relation to standard curves using the FCAP Array software (BD Biosciences).Sera from the three groups of rats . Data were compared with adequate non parametric Kruskal-Wallis ANOVA on Ranks to assess statistical significance with Sigma Stat software . ABP has anti-inflammatory and immuno-regulatory therapeutic effects in a mouse model of chronic arthritic inflammation when administered by systemic routes [ABP in a robust model of acute inflammation, namely the EIU in rats, performing a loco-regional administration of the molecule by the intra-vitreal route.Previously we have shown that dendrimer c routes , making c routes . In thisABP was evaluated after ocular administration in rats. The NOAEL dose was established at 20 µg/eye. The intensity of the clinical ocular EIU disease was evaluated by funduscopy and SLE 24 h after induction by LPS injection. We have shown that a single intra-vitreal administration of dendrimer ABP at the time of LPS injection induces a significant reduction of ocular inflammation. The strongest effect was observed at the lowest dose (2 µg/eye), and the effect dendrimer ABP was not found to be statistically different from the effect of the “gold standard” dexamethasone at higher dose (20 µg/eye).The tolerability of the dendrimer ABP at 2 µg/eye. IL-6 and IL-17 concentrations tend clearly to be reduced by this low dose, even though the reduction observed is not significant. Nevertheless, dendrimer ABP does not down-regulate important pro-inflammatory cytokines such as TNFα and IL-1β. Moreover, in serum, both dexamethasone and dendrimer ABP induced a strong increase of IL-10, the paradigm of anti-inflammatory and immuno-modulatory cytokines. This latter result suggests that these anti-inflammatory drugs might undergo a systemic passage while administered by a loco-regional route [We have also demonstrated that cytokine dosage in ocular fluids is also consistent with an anti-inflammatory effect of dendrimer al route ,23.ABP targets monocytes and triggers their anti-inflammatory activation [ABP in the EIU model may be mediated through anti-inflammatory activation of monocytes/macrophages, leading to systemic IL-10 production. Moreover, we have also shown that dendrimer ABP inhibits human CD4+ T lymphocytes [ABP in this model.In the EIU rat model, the LPS administration may induce ocular inflammation by stimulating the production of pro-inflammatory cytokines by activated monocytes/macrophages . We havetivation ,7. Therephocytes , these cABP has a significant anti-inflammatory activity in a clinically relevant rat model of anterior uveitis. This idea is supported by the fact that dendrimer ABP at 2 µg/eye is as active as “gold standard” dexamethasone at 20 µg/eye. This strengthens the anti-inflammatory and immuno-regulatory properties of dendrimer ABP for both chronic and acute inflammatory diseases, and makes it a possible drug-candidate for inflammatory diseases in ophthalmology.Taken together these results indicate that topical administration of dendrimer


M entries, each represented by n bits, the method requires O(n) qubits and O(Mn) steps. With post-selection at an additional cost, our method can also store continuous data as probability amplitudes. As an example, we present a procedure to convert classical training data for a quantum supervised learning algorithm to a quantum state. Further improvements can be achieved by reducing the number of state preparation queries with the introduction of quantum forking.A prerequisite for many quantum information processing tasks to truly surpass classical approaches is an efficient procedure to encode classical data in quantum superposition states. In this work, we present a circuit-based flip-flop quantum random access memory to construct a quantum database of classical information in a systematic and flexible way. For registering or updating classical data consisting of  The ability to efficiently convert classical data into quantum states is essential in many algorithms with complex data sets, such as quantum searching3, collision finding4, and quantum Fourier transform5. The demand for such ability has continued to grow with recent discoveries of quantum algorithms for data analysis and machine learning applications with large classical data10. Quantum simulation also requires the preparation of a quantum register in the initial physical state of the simulated system11. One promising avenue is to use quantum random access memory (QRAM)12, a device that stores either classical or quantum data with the ability to query the data with respect to superposition of addresses. The bucket brigade (BB) model for QRAM proposed in refs13 requires O(M) qutrits for routing, and O(M) classical or quantum memory cells for M binary data. The content of multiple data cells can be returned in superposition with only The theory of quantum information processing promises to accelerate certain computational tasks substantially. In practice, the computational cost of generating an arbitrary quantum input stateM classical data represented as n bits of information and bl is the attribute of O(n) qubits and O(Mn) quantum operations that are commonly found in many known algorithms. The probability amplitudes can be modified by post-selection at an additional cost of repeating the process and single qubit measurement. In addition, the FF-QRAM architecture can serve as a building block for the classical-quantum interface.Since quantum operations are applied directly to the qubits that form a QRAM as the state preparation is followed by a quantum algorithm, it is favorable to build a QRAM based on the quantum circuit model. At the same time, a QRAM should be a good interface to classical data for big data applications. In this work, we propose a flip-flop (FF) QRAM, which is constructed with the standard circuit-based quantum computation and without relying on a routing algorithm. The FF-QRAM can read unsorted classical data stored in memory cells, and superpose them in the computational basis states with non-uniform probability amplitudes to create a specific input state required in a quantum algorithm. Also, the classical information stored in the quantum state can easily be updated with the same FF-QRAM process. The cost for writing or modifying 14. Quantum forking is a framework to split unitary processes in superposition, with which the number of QRAM queries can be reduced in certain applications.A quantum state prepared by QRAM as an input to a specific algorithm cannot be reused once measured (the quantum measurement postulate), nor be copied (the no-cloning theorem) for another task. Thus, in general, the QRAM cost seems unavoidable per algorithm run, even when performing a set of algorithms with an identical input state. Here we introduce a process of quantum forking inspired by process forking in computer operating systems, which creates a child process that can evolve independentlyM is the number of data. For big data applications, a typical quantum representation of l denote a data entry and the corresponding label, respectively10. The probability amplitude, bl, can encode continuous data as required in some applications15, or represent the normalized occurrence of the data entry M numbers of n-bit data, n + m qubits are sufficient to realize the QDB, where n and A quantum superposition state prepared with respect to classical data for quantum computation can be referred to as quantum database (QDB). In most general form, a QDB can be expressed asn + m)-qubit bus state to encode a big data class database. The bus qubit state can be arbitrary, and it defines which computational basis states, |j〉B, are accessed with probability amplitudes, D asB (R) indicates the bus (register) qubit, and the register qubit can include the probability amplitudes for encoding the analog data. The FF-QRAM is implemented systematically with standard quantum circuit elements, which include the classically-controlled Pauli X gate, n-qubit controlled rotation gate, CnRp(θ). The CnRp(θ) gate rotates the target qubit by θ around the p-axis of the Bloch sphere only if all n control qubits are 1.The FF-QRAM is used to generate a QDB as follows. Consider a quantum computer with an (n + 1) qubits in the process of writing the lth data entry, observed at the sth step in Fig. The underlying idea of the FF-QRAM model is depicted in Fig. mentclass2pt{minimθl), which is data dependent. In some instances, such as in the distance-based quantum classifier10, the post-selection success probability can be improved by pre-processing the classical data so that θl) flip-register-flop steps, the total FF-QRAM cost must include the resource overhead for the register operations. In fact, the number of elementary gates needed for this step can dominate the runtime of the entire QRAM process. Thus efficient realization of CnRp(θ) is critical for the practicality of our scheme. Though the optimal circuit depth reduction can be carried out based on the naturally available set of gates in a specific experimental setup, and is beyond the primary scope of this paper, we briefly mention some examples on how to implement CnRp(θ) here. If energy splittings between all pairs of the computational basis states are distinct, then in principle, a resonant pulse at the frequency corresponding to the energy difference between CnRp(θ). But this condition becomes exponentially challenging to satisfy in practice as the number of qubits increases. On the other hand, we can decompose the controlled rotation as Ry(θ/2) CnNOT nNOT gate can be further decomposed into 2n − 3 Toffoli gates with n − 2 ancilla qubits prepared in 16. Other methods for implementing CnNOT using O(n) number of elementary gates and ancillary space are discussed in refs18. The circuit optimization in terms of Clifford and T gates can be performed using the techniques presented in refs20.In addition to ε, and remains unchanged with probability nNOT, 2n − 1 qubits undergo M classical bit strings of length n with arbitrary probability amplitudes is M classical bit strings with arbitrary probability amplitudes, assuming ps of the total QRAM process. A milder assumption that the imperfect CnRp(θ) operation causes independent errors on n + 1 qubits yields a better success probability, We investigate the robustness of the FF-QRAM shown in Fig. entclass1pt{minima23 can be employed to enhance the accuracy. In contrast, if quantum error correction is applied to BB-QRAM, all routing components are activated at a physical level and make the scheme equivalent to the conventional fanout architecture24. In addition, depending on the physical setup, the quantum circuit can be further optimized using various gate decomposition techniques26.Since our scheme is based on the quantum circuit model, fault-tolerant quantum error correction techniquesM denotes the number of training data samples8. The quantum circuit for preparing this QDB is depicted in Fig. i, where without loss of generality, M and N are assumed to be powers of two. An equal superposition state for log2(M) and log2(N) qubits is used as the bus qubit for providing the computational basis states k and i, respectively. The jth element of y-axis rotation of the register qubit. Note that the gates shaded in gray are included only to show the full flip-flop process for addressing a specific computational basis state, but they can be omitted in the implementation. The state shown in Eq. (O(MN) flip-register-flop operations.As an example, we demonstrate the FF-QRAM process for preparing a training data state in the quantum support vector machine. The classified training examples, n-qubit QDB state n-qubit state s in Fig. n-qubit swap gate between Here, we introduce a concept of quantum forking (QF) with which a qubit can undergo independent processes in superposition. This can be utilized as a means to reduce the number of QRAM queries in certain applications. Let us consider a quantum state n-qubit data block if the control qubit is 0, and in the second n-qubit data block if the control qubit is 1. Then by applying two unitary evolutions activated by different computational basis states of the control qubit to each n-qubit block, In other words, the QDB is encoded in the first 27 and the inner product calculation. Here we focus on the inner product evaluation problem as an example. The inner product between 28. Alternatively, starting from the state shown in Eq.  additional gates, but reduces the number of QRAM queries by a factor of ~1/2. Note that the conventional swap test can only estimate the magnitude of the inner product. Thus the QF based approach not only reduces the number of QRAM queries, but also allows for the determination of the sign of the inner product. This is a consequence of an important property of the QF circuit; since different unitary operators can be applied to each branch (subspace), the global phase that a unitary operator introduces become distinguishable. Clearly, the quantum circuit shown on the left side of Fig. 27.Finally, the probability of measuring the control qubit in d (or log2(d) qubits), and O(nd) gates.Generalizing above idea, a quantity such as H3 represents the qutrit Hadamard operation for preparing the equal superposition of the three computational basis states. This circuit produces an entangled state The quantum forking for implementing three different unitary processes in superposition is depicted in Fig. n-bit classical data with arbitrary probability amplitudes stored in M memory cells into quantum format using O(n) qubits and O(Mn) flip-register-flop steps. The versatility of the architecture allows to create a complex data structure via encoding any classical information, either discrete or continuous, as quantum bits or as probability amplitudes of a quantum state. An example of the amplitude encoding is the application to a quantum state generation for a quantum support vector machine algorithm in which the training data is represented with the probability amplitudes as shown in Fig. CnRp(θ). For the uniform weight which is, for example, encountered in the parity learning algorithm30, the multi-qubit controlled gate is simply CnNOT. For the amplitude encoding, the final QDB state is obtained by post-selecting on the register qubit being 20 introduces a procedure inspired by classical alias sampling to assign the probability amplitude μ + 2n + O(1) ancilla qubits, where μ-bit binary approximation to the desired non-negative real value, ρ. In ref.11, adiabatic-diabatic state preparation is used to generate superposition states with squared amplitudes.Encoding large classical data into a quantum database must be done efficiently in a way that the potential advantages of the quantum algorithms for big data applications do not vanish. We proposed the flip-flop QRAM, a systematic architecture, for preparing a quantum database using the quantum circuit model. The circuit-based construction is imperative since it provides flexibility and compatibility with existing quantum computing techniques. Our process can register L identical QRAM processes in parallel. Then the success probability of the post-selection improves by a factor of L while also increasing the number of qubits and the gates by the same factor. Note that the time complexity remains the same. Second, the QDB is not reusable once it is consumed by a quantum algorithm since the measurement collapses the state. Motivated by the above, we introduced the concept of quantum forking that allows to reduce the number of QRAM queries in some instances, in particular, when evaluating the inner product. Finding other instances for which the quantum forking can reduce the number of QRAM calls, even by a constant amount, remains an interesting open problem.We point out potential solutions to several issues for meaningful applications of QRAM. First, when the FF-QRAM process leaves the last term in Eq.  that cornNOT gate can be decomposed into a Cn−1NOT and a C2NOT (Toffoli) using an ancilla qubit prepared in n = 4 as an example. Then by recursion, CnNOT can be realized using 2n − 3 Toffoli gates and n − 2 ancilla qubits prepared in n − 2 Toffoli gates are added after the Toffoli gate for conditionally flipping the target qubit in order to unentangle the ancilla qubits from the system. The quantum circuit can be rearranged to further reduce the depth as shown in the last step in Fig. The CCnRy(θl) and before CnRy(θl+1) can be merged. The combined operation flips the jth qubit only if M classical data of length n is n(M + 1). Each CnRy(θ) uses two single qubit gates and two CnNOT gates. In the CnNOT implementation described above  undergo We assume that the ove Fig. , 2n − 1 τ that are subject to noise can be counted asTherefore, the total number of time steps CnRy(θ) can be implemented with only n + 1 independent errors, then τ can be further reduced to If


Word embedding technologies, a set of language modeling and feature learning techniques in natural language processing (NLP), are now used in a wide range of applications. However, no formal evaluation and comparison have been made on the ability of each of the 3 current most famous unsupervised implementations  to keep track of the semantic similarities existing between words, when trained on the same dataset.The aim of this study was to compare embedding methods trained on a corpus of French health-related documents produced in a professional context. The best method will then help us develop a new semantic annotator.Unsupervised embedding models have been trained on 641,279 documents originating from the Rouen University Hospital. These data are not structured and cover a wide range of documents produced in a clinical setting . In total, 4 rated evaluation tasks were defined  and applied on each model, as well as embedding visualization.Word2Vec had the highest score on 3 out of 4 rated tasks , particularly regarding the skip-gram architecture.Although this implementation had the best rate for semantic properties conservation, each model has its own qualities and defects, such as the training time, which is very short for GloVe, or morphological similarity conservation observed with FastText. Models and test sets produced by this study will be the first to be publicly available through a graphical interface to help advance the French biomedical research. The use of clinically derived data from electronic health records (EHRs) and other clinical information systems can greatly facilitate clinical research as well as optimize diagnosis-related groups or other initiatives. The main approach for making such data available is to incorporate them from different sources into a joint health data warehouse (HDW), thus containing different kinds of natural language documents, such as prescription, letters, surgery reports—all written in everyday language .Clinical named entity recognition (NER) is a critical natural language processing (NLP) task to extract concepts from named entities found in clinical and health documents (including discharge summaries). A semantic health data Warehouse (SHDW) was developed by the Department of Biomedical Informatics of the Rouen University Hospital (RUH), Normandy, France. It is composed of 3 independent layers based on a NoSQL architecture:A cross-lingual terminology server, HeTOP, which contains 75 terminologies and ontologies in 32 languages A semantic annotator based on NLP bag-of-word methods (ECMT) A semantic multilingual search engine To improve the semantic annotator, it is possible to implement deep learning techniques to the already existent one. To do so, a new text representation, which keeps the most semantic similarities existing between words, has to be designed to fit the input of neural networks algorithms (text embedding).distributional hypothesis.In NLP, finding a text representation that retains the meaning proximities has always been a moot point. Indeed, the chosen representation has to keep the semantic similarities between different words from a corpus of texts to allow indexation methods to output a correct annotation. Thus, the representation of a unique token has to show the proximity with other related meaning concepts , as illustrated in the quotation “You shall know a word by the company it keeps” , now knon dimensions, n representing the vocabulary size). In fact, a compact and precise representation of words could bring several benefits. First comes the computational aspect. Computers are way better to perform operations on low-dimensional objects. This then permits to calculate the probability of a specific concept to appear close to another one. Moreover, the vectors’ dimensions created to represent a word can be used to fit this word in a space and thus make distance comparisons with other tokens. Current unsupervised embedding techniques provide dense and low-dimensional information about a word, either with count-based or predictive-based methods  + Term 3 ~ Term 4)). Then, the operation was performed using vectors Term 1, Term 2, and Term 3 extracted from each model. The resulting vector was compared with the Term 4 vector, the operation being considered as correct if this Term 4 vector was found to be the closest one regarding the cosine distance with the operation resulting one, indicating a semantic similarity between Term 3 and Term 4, similar to the one between Term 1 and Term 2.Mikolov’s paper presenting Word2Vec showed that mathematical operations on vectors such as additions or subtractions are possible, such as the famous  were used for model pretraining. Then, this resulting embedding was trained a second time on the documents from the RUH without changing any parameter. All of the automatic tests were performed for this model a second time to assess if the added academic data improved the model’s quality regarding our evaluation.SD 207.42). The 10 most common words are listed in In total, 641,279 documents from the RUH have been de-identified and preprocessed. With regard to the vocabulary, texts have been split into 180,362,939 words in total, representing 355,597 unique tokens. However, this number can be pondered with 170,433 words appearing only once in the entire corpus . In total, 50,066 distinct words were found more than 20 times in the corpus, thus present in the models (minimum count parameter set to 20). On average, each document contains 281.26 words (K=5). To visualize their distribution on 2 dimensions, t-SNE algorithm had been used (These documents were decomposed using the Term-Frequency Inverse-Document-Frequency (TF-IDF) algorithm that resulted in a frequency matrix. Each row, representing an article, had been used to cluster those documents with a kMeans algorithm (number of classes een used  29]..K=5). ToThose main classes were well separated, thus the vocabulary itself contained in the documents from the HDW was sufficient to clusterize each type of text. However, discharge summaries, surgery, or procedure reports were a bit more mixed because of the words used in these kinds of context . With regard to drug prescriptions and letters to a colleague or from a general practitioner, they present a more specific vocabulary , involving more defined clusters for these 2 groups.Regarding the training time, models were very different. GloVe was the fastest algorithm to train with 18 min to process the entire corpus. The second position was occupied by Word2Vec with 34 min and 3 hours 02 min . Finally, FastText was the slowest algorithm with a training time of 25 hours 58 min with SG and 26 hours 17 min with CBOW .context || target pairs highly increases the time to go through all possibilities.GloVe performs much better in terms of computational time because of the way it handles the vocabulary. It is stored as a huge co-occurrence matrix and thanks to its count-based method, which is not computationally heavy, it can be highly parallelized. It was expected that FastText would take a lot of time to train, because of the high number of word subvectors it creates. However, for Word2Vec, the difference between the 2 available subarchitectures is highly visible (33 min to 3 hours 02 min). This difference could come from the hierarchical softmax and one-hot vector used by the CBOW architecture, which reduces the usage of the CPU. With SG, the minibatch parsing of all the The total number of UMNSRS pairs successively retrieved by each model has been extracted . The percentages of validated pairs from the UMNSRS datasets are presented in the With regard to the odd one similarity task, models are quite different . Word2VeWith regard to the subarchitectures presented by both Word2Vec and FastText, the SG always performed better than the CBOW, possibly because of the negative sampling. Indeed, the studied corpus is quite heterogeneous and words can be listed as items  instead of being used in correct sentences. Thus sometimes, the complete update of vectors’ dimensions generates non-senses in the models .The evaluation focused on 1796 terms  rated from 0 to 2 by 2 evaluators. First, the agreement between CM and SJD was assessed with a weighted kappa test . A kappaMoreover, to assess if human evaluators remained coherent regarding the cosine distance computed by each model, the average note given by the 2 evaluators was compared with the average of the cosine distance computed for each model . Word2VeTo go further, the cosine distances between the 112 sent concepts and the 1796 returned were plotted for each of the 3 modalities rated by the evaluators . In fact, allowing to check if the similarity between Term 1 and Term 2 is the same as the one between Term 3 and Term 4. These operations have been defined to cover a wide range of subjects .A list of 6 mathematical operations has been defined with the help of an MD and a university pharmacist , while CBOW only reached (3/6)). FastText, independently of the architecture studied, obtained a score of (3/6). GloVe got the lowest score by reaching (2/6).Each operation mélanome [melanoma] and adénome [adenoma]) were cited far from their localization . This distance may be too high for the context-window size (7 words).Interestingly, no operation has been failed by the 5 models, indicating that none of them is simply not logical or just too hard to perform for word embedding models. Operation 2 has been missed by both Word2Vec and FastText SG, whereas CBOW architectures succeeded to perform it for both algorithms. In the corpus, tumors . The subword decomposition performed by this algorithm was keeping track of the context, but was not as accurate as Word2Vec SG in this task. This imbalance was not compensated by the SG architecture, which performed better for Word2Vec, indicating that this subword decomposition has a really strong impact on the embedding.(cardiologie - coeur) + poumon ~ pneumologie(cardiology - heart) + lung ~ pneumology(mélanome - peau) + glande ~ adénome(melanoma - skin) + gland ~ adenoma(globule - sang) + immunitaire ~ immunoglobuline(corpuscle - blood) + immune ~ immunoglobulin(rosémide - rein) + coeur ~ fosinopril(furosemide - kidney) + heart ~ fosinopril(membre - inférieur) + supérieur ~ bras(limb - lower) + upper ~ arm(morphine - opioide) + antalgique ~ perfalgan(morphine - opioid) + antalgic ~ perfalganAs a visual validation, t-SNE algorithm was applied on vectors extracted from each of the 5 models. To investigate how word vectors are arranged, clusters had been manually searched on the projection. Word2Vec clustered words with a good quality regarding the context they could be used in. Both SG and CBOW architectures had logical word clusters, for example, related to time .an [year] to 8 for semaines [weeks]) or the composition of letters (no letters in common between the 2 neighbors semaine [week] and jour [day]).Many other clusters were found by reducing the dimension of both Word2Vec SG and CBOW results; some are showed on By looking at the dimensional reduction of vectors produced by GloVe, it is visible how co-occurence matrix used by this algorithm is affecting the placement of vectors in the VSM. In fact, words often used close to each other  are clusterizing well. In the group given as an example in With regard to FastText, it is interesting to notice that clusters of words used in a similar context were found but other variables do influence the spatial arrangement of the vectors a lot when projected on 2 dimensions: word size and composition. Indeed, as seen on the With regard to the global shape of the 5 projections on the So far, Word2Vec with the SG architecture showed the best results in average . Thus, aWhen this model trained on 2 different datasets is compared with the initial Word2Vec model (without any pretraining), scores were not changed with regard to the cosine and odd one tests . Interestingly, the grade coming from analogy-based operations decreased, lowered from 5/6 to 3/6. This could come from the fact that documents used for pretraining (scientific articles) were highly specialized in a domain, leading to already strongly associated vectors.In this study, the 3 most famous word embeddings have been compared on a corpus of challenging documents  with 5 different evaluating tasks. The positive and negative semantic relationships have been assessed, as well as the word sense conservation by human and analogy-based evaluation.Gensim, which could have brought a bias in this study. This model is computing a cosine distance closer to 1 in average between queried word and close ones, whereas human judgment shows the lowest grade. With regard to FastText, it is interesting to notice that the morphological similarities are kept in account in the vector space creation. In fact, word clusters are highly impacted by the word’s composition in letters and by its size. However, the subvector decomposition of words allows this kind of model to be queried by words absent in the original training corpus, which is impossible with others. Therefore, this model could be used for orthographic correction or acronym disambiguation, for example.The training in our 600,000 of challenging documents showed that Word2Vec SG got the best score for 3 on the 4 rated tasks (FastText SG is the best regarding the cosine one). These results are coherent with those obtained by Th et al, who compared Word2Vec and GloVe with the cosine similarity task . More spThe medical corpus used as a training set for these embedding models is coming from a real work environment. First, finding a good evaluation for embeddings produced in such a context is a hard task. The performances shown by some models trained on scientific literature or on other well-written corpus should be biased regarding their utilization on a very specific work environment. Second, based on our results, an amount of 26.1% of unique tokens found in the health-related documents are not present in an academic corpus of scientific articles, indicating a weakness of the pretrained embedding models. Documents produced in a professional context are highly different compared with this kind of well-written texts. Finally, in this study, pretraining an embedding with an academic corpus and then on the specific one does not improve the model’s performances. It even lowers the score associated to analogy-based operations, indicating strongly associated vectors in the VSM, which leads to a loose of the inherent plasticity of this kind of model to deeply understand the context of a word.There are a few limitations in our study. First, other embedding models, newly released, could have been compared as well , representing 72.3% of the total number of word pairs searched that cannot be found in the models.Regarding the cosine annotation, low scores could be explained by the number of occurrences of each term from the 625 words pairs in the corpus of texts. The UMNSRS-Rel dataset contains 257 unique terms for 317 word pairs, whereas the UMNSRS-Sim contains 243 terms for 308 word pairs. First, 128 words in total (25.6%) have been found less than 20 times regarding all of the 641,279 documents, thus being absent in the model because of the disulfirame). The natural medical language used in the RUH by the practitioners prevents some words to be found: use of an acronym  or of a synonym . Another explanation could come from the fact that some associations defined in those UMNSRS datasets can be true in an academic context, but will be very rarely found in a professional context.Most of the words absent from the models are drugs’ molecular names, whereas practitioners from the RUH often use the trade names to refer to a drug  is mainly composed of clinical symptoms or diseases. This validation corpus seems to be just not suitable to investigate the quality of embedding trained on such a corpus.With a median number of occurrences of 230 in the entire corpus of health documents, 176 words (28.1%) have been found more than 1000 times. Whereas the biggest proportion of the low-frequency words was composed of drugs or molecules names, the high-frequency group of words (up to 134,371 times for the word In our case, Word2Vec with the SG architecture got the best grade in 3 out of the 4 rated tasks. This kind of embedding seems to preserve the semantic relationships existing among words and will soon be used as the embedding layer for a deep learning based semantic annotator. More specifically, this model will be deployed for semantic expansion of the labels from medical controlled vocabularies. To keep the multilingual properties of the actual annotator, a method of alignment between the produced embedding and other languages will also be developed. Other recently tested unsupervised embedding methods exhibit a certain quality, but their ability to preserve the semantic similarities between words seems weaker or influenced by other variables than word context.As soon as the paper is submitted, any end user will be able to query the word embedding models produced by each method on a dedicated website as well as to download high quality dimension reduction images and test sets . This em


Age-related cataract (ARC) is one of the major causes of visual impairment and reversible blindness worldwide. Accumulating evidence has revealed that circular RNAs (circRNAs) are involved in multiple regulatory processes in various ocular diseases. However, the expression profile, regulatory roles, and underlying mechanisms of circRNAs in ARC remain largely unknown. Herein we deep-sequenced circRNAs of anterior lens capsules from normal and ARC lenses, and detected 23,787 candidate circRNAs. Of these, 466 were significantly differentially expressed, and a higher correlation in down-regulated circRNAs between ARC and diabetic cataract was observed compared with up-regulated ones. Subsequent bioinformatics analysis disclosed that certain differentially expressed circRNAs participated in oxidative stress and apoptosis-related signaling pathways in ARC. Notably, the level of circZNF292 was significantly decreased, while miR-23b-3p was significantly increased in ARC. The target region prediction and dual-luciferase reporter assays proved that circZNF292 acted as a competitive endogenous RNA to regulate the expression of anti-oxidative genes through competing with miR-23b-3p. Our results indicate that circZNF292, a down-regulated circRNA in the anterior lens capsule of ARC patients, may be involved in resistance to oxidative damage and apoptosis of lens epithelial cells by sponging miR-23b-3p, providing a potential target for prevention and treatment of ARC. Cataract is one of the most common eye diseases which result in visual impairment and reversible blindness , 2. TherIn previous studies on the pathogenesis of ARC, oxidative stress was demonstrated to directly cause lens opacity and assumed to be a key factor during the development of cataracts , 8. FromWith the rapid advance of high-throughput sequencing technology, the role of circular RNAs (circRNAs), which emerge as vital regulators in various diseases, has drawn increasing attentions –17. UnliMoreover, numerous non-coding RNAs participate in oxidative damage during the cataract formation –34. ChenIn the current research, we explored the underlying mechanisms of circRNAs in the process of resisting oxidative damage by characterizing the interactions among circRNAs, miRNAs, and mRNAs in ARC for the first time. Among the differentially expressed circRNAs, circZNF292 was disclosed to act as a competitive endogenous RNA (ceRNA) of miR-23b-3p and be involved in reducing the oxidative damage to LECs by binding to anti-oxidative genes, thereby delaying the occurrence and development of ARC.To understand the regulatory roles of circRNAs in ARC, we first characterized the expression profile of circRNAs in anterior lens capsules. Briefly, we performed RNA sequencing (RNA-Seq) of ribosomal RNA (rRNA)-deleted total RNAs from normal  and ARC anterior lens capsules   on an IlP < 0.05) were set to elect differentially expressed circRNAs  was found to be significantly down-regulated in the ARC sample tissues [In our study, we detected circRNA expression profiles in ARC in detail using second generation sequencing technology to explore their potential clinical value. A total of 466 significantly different circRNAs were detected, 92 of which were newly detected molecules. Similarly, in our sequencing data, circHIPK3 , aged 54 to 81 years , who underwent ARC surgery at our institution. All these patients had no diabetes, hypertension or other ocular diseases. The capsules were removed by the same experienced surgeon (YH) during continuous curvilinear anterior capsulorhexis of cataract surgery. Moreover, nine transparent anterior lens capsules from healthy donor eyes were used as normal controls. All samples were immediately flash-frozen in liquid nitrogen before stored at -80 °C. Because the content of RNAs of a single lens anterior capsule was not adequate for RNA sequencing, three samples were combined for RNA extraction. Hence there were six replicates in the ARC group and three replicates in the control group . For subTotal RNAs were extracted from frozen anterior lens capsule tissues using TRIzol reagent  in accordance with the instructions. The concentration of total RNAs was measured by a NanoDrop instrument , and the ratio of OD260/OD280 (between 1.8 and 2.1) was used as an indicator of RNA purity. The integrity of RNAs was also detected on the denaturing agarose gel electrophoresis according to the morphology of the 28S and 18S rRNA bands. Then library construction for sequencing was performed. Briefly, rRNAs in total RNAs were removed, and the purified RNAs were reverse-transcribed into complementary DNAs (cDNAs), adaptor ligated, and PCR amplified following the instructions of the TruSeq Stranded Total RNA Library Prep Kit (Illumina). RNA libraries were quality-controlled and quantified using the BioAnalyzer 2100 system  before sequenced on the Illumina HiSeq4000 Platform with a read length of paired-end 150 bp.http://www.circbase.org) and circ2Trait [http://gyanxet-beta.com/circdb/) were used to annotate the identified circRNAs.The 3' adaptor sequences were trimmed with cutadapt software (v1.9.3) . Clean rrc2Trait    was usedCompared with the same control group, we performed RNA-seq on the human anterior capsule tissues of patients with ARC and DC . R packehttp://www.geneontology.org) and KEGG (http://www.genome.jp/kegg) enrichment analyses on the host genes of differentially expressed circRNAs. GO developed a structured, controlled vocabulary to describe genes and gene product attributes in organisms. The ontology covered molecular function, biological process, and cell component. Through the KEGG pathway analysis of host genes, we inferred the signaling pathways involved in circRNAs and their biological functions. The P value was obtained using fisher’s exact test, with a recommended cut-off at 0.05.We performed GO (https://web.archive.org/web/20110222111721/http://starbase.sysu.edu.cn/), which provides miRNA-target interaction prediction based on high-throughput CLIP-Seq data [To clarify the role of differential circRNAs in cataracts, miRNA targets for circRNAs were predicted using target prediction software based on miRanda and TargetScan . StarBase . qRT-PCR was performed on the ViiA 7 Real-time PCR System (Applied Biosystems) using the qPCR SYBR Green Master Mix (Applied Biosystems). Specific primers for circRNAs were designed by primer 5.0 according to the sequence of the linear transcripts. Primer sequences of selected circRNAs and miRNA are shown in http://genome.ucsc.edu/cgi-bin/hgGateway) and circPrimer1.2 (http://www.bioinf.com.cn/) provided a visual representation of the circZNF292 composition and its location on the parental genes.To further elucidate the functional role of circRNAs, we selected circZNF292, which was markedly down-regulated in ARC plasma tissues, for further analysis. TargetScan and StarBase were applied to predict the mRNA targets of miRNAs. Based on a previous report , oxidatiRenilla were detected 48 hours after transfection according to the manual of the Dual-Luciferase Reporter Assay System (Progema), and the relative fluorescence value was calculated.A dual-luciferase reporter assay was performed to confirm the direct binding of miR-23b-3p and circZNF292. The wild-type and mutant sequences of circZNF292 were subcloned into multiple cloning regions (1640–1674 bp) of psiCHECK-2 luciferase reporter vectors (Progema). Then target-site containing plasmids, together with miR-23b-3p mimics or miRNA negative controls, were co-transfected into cells with Lipofectamine 2000 transfection reagent (Thermo Fisher). The fluorescence activities of firefly and Anterior lens capsules used in this study were collected from patients undergoing surgery for ARC and healthy donor eyes provided by the eye bank of our institution. The study was performed in accordance with the tenets of the Declaration of Helsinki. The protocol was reviewed and approved by the Ethics Committee of Shandong Eye Institute. We informed the patients of the use of their specimens and obtained their consent.Supplementary Table 1